Studying Studying EM Theory?

Is it possible to study Electromagnetic theory without knowing the concepts of classical mechanics. I have studied Newtonian mechanics but does not have any idea about Lagrange and Hamiltonian mechanics. I am concentrating on the below topics in Electromagnetic theory:

You appear to be making a HUGE jump here. The topics you listed require a strong mathematics background, well beyond what your intro Newtonian mechanics class requires. You don't necessarily have to study mechanics first but the math is a must. What is your mathematics background like?

Generally you would start with intro electricity and magnetism. Single variable calculus should be sufficient for your first exposure to these topics.

I come from engineering background... so i have pretty good knowledge on Differential calculus, Integral calculus, vector calculus(like stoke's theorem), PDE.... i think even if i miss some topics in mathematics i can fill the gap. However, my worry is some what related to "Physics part". Am i able to grasp the conceptual part of EM theory??(without knowing Lagrange and Hamiltonian mechanics??)

This list, it looks like a list of topics to be covered in a course, taken out of a catalog of some type. Is this right? Are you trying to find out if you can take this course, even though it lists as a pre-requisite upper-level mechanics? My feeling here is that you saw that, looked through the list of topics on that course, and saw the two things you didn't know about, and asked.

If so, my answer would be, ask the professor. E&M courses can vary wildly in difficulty depending on the level. If you're looking to jump in at the top, and you don't have a physics background, well, that's going to be tough.

It is very unlikely that you will need to know anything about Hamiltonians etc in order to study any of the topics in that list.
The Hamiltonian/Lagrangian formulation is not used nearly as much as most people seem to think. It is mainly -not surprisingly- used in mechanics and advanced quantum mechanics (you don't really need to have any "deep" knowledge of analytical mechanics in order to understand basic quantum mechanics, you need to know what H represents and that is about it, the rest is linear algebra).
I suspect most mechanical engineers know more about the topic than your average physicist.

I've never even seen a Hamiltonian in an E&M textbook, so unless it is explicitly listed as a prerequisite you don't need to worry about it.

I've never even seen a Hamiltonian in an E&M textbook, so unless it is explicitly listed as a prerequisite you don't need to worry about it.

That is too bad, there is a little bit in Jackson's Classical Electrodynamics with a reference to Barut's Electrodynamics and Classical Theory Fields and Particles for more. There is no particular need to have seen it in a mechanics context before hand. Some books and courses on Lagragian mechanics do not even mention the hamiltonian which is even more troubling. Electrical engineers often learn about EM without knowing much about mechanics.